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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 732164, 21 pages
http://dx.doi.org/10.1155/2011/732164
Research Article

Bounds of Double Integral Dynamic Inequalities in Two Independent Variables on Time Scales

College of Science Research Centre, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

Received 4 October 2011; Revised 29 October 2011; Accepted 31 October 2011

Academic Editor: Delfim F. M. Torres

Copyright © 2011 S. H. Saker. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Our aim in this paper is to establish some explicit bounds of the unknown function in a certain class of nonlinear dynamic inequalities in two independent variables on time scales which are unbounded above. These on the one hand generalize and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of partial dynamic equations on time scales. Some examples are considered to demonstrate the applications of the results.